Math, asked by shSaddam6283, 9 months ago

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:
f (x) = x²

Answers

Answered by shravani7894
3

Answer:

ANSWER

Maximum or minimum can be seen by using derivatives.

Step 1: First find first derivative of the function

Step 2: Put it equal to zero and find x were first derivative is zero

Step 3: Now find second derivative

Step 4: Put x for which first derivative was zero in equation of second derivative

Step 5: If second derivative is greater than zero then function takes minimum value at that x and if second derivative is negative then function will take maximum value at that x. If Second derivative is zero them it means that this is the point of inflection.

g

(x)=

2

1

x

2

1

Putting this equal to zero, we get

g

(x)=

2

1

x

2

1

=0

⇒x=±2.

Please note that −2 is not in the domain of given function so it is of no use to us

Now let's see the double derivative of this function.

f

′′

(x)=

x

3

4

At x=2

f

′′

(2)=

2

3

4

=

2

1

Which is positive, so function will take minimum value at x=2

Minimum value is given by

f(x)=

2

2

+

2

2

=2

hope it's helpful to u

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